(f+9)(x)=f(x)+g(x)

Solution for (f+9)(x)=f(x)+g(x) equation:

Simplifying
(f + 9)(x) = f(x) + g(x)

Reorder the terms:
(9 + f)(x) = f(x) + g(x)

Reorder the terms for easier multiplication:
x(9 + f) = f(x) + g(x)
(9 * x + f * x) = f(x) + g(x)

Reorder the terms:
(fx + 9x) = f(x) + g(x)
(fx + 9x) = f(x) + g(x)

Multiply f * x
fx + 9x = fx + g(x)

Multiply g * x
fx + 9x = fx + gx

Add '-1fx' to each side of the equation.
fx + -1fx + 9x = fx + -1fx + gx

Combine like terms: fx + -1fx = 0
0 + 9x = fx + -1fx + gx
9x = fx + -1fx + gx

Combine like terms: fx + -1fx = 0
9x = 0 + gx
9x = gx

Solving
9x = gx

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1gx' to each side of the equation.
-1gx + 9x = gx + -1gx

Combine like terms: gx + -1gx = 0
-1gx + 9x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1g + 9) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0
Subproblem 2
Set the factor '(-1g + 9)' equal to zero and attempt to solve:

Simplifying
-1g + 9 = 0

Reorder the terms:
9 + -1g = 0

Solving
9 + -1g = 0

Move all terms containing x to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + -1g = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1g = 0 + -9
-1g = 0 + -9

Combine like terms: 0 + -9 = -9
-1g = -9

Add 'g' to each side of the equation.
-1g + g = -9 + g

Combine like terms: -1g + g = 0
0 = -9 + g

Simplifying
0 = -9 + g

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}